Generalized real-time thermal model

Abstract

A generalized real-time thermal model of an induction motor produces values indicative of the transient and steady state temperature condition of the motor. Each of these values is compared with respective predetermined limits and power to the motor is removed when any value exceeds its respective limit in order to prevent damage to the motor.

What is claimed is: 
     
       1. A method for protecting an induction motor from excessive thermal overloads with the aid of a general purpose microprocessor, comprising: defining an electrical thermal analog of the motor, wherein the thermal analog includes copper thermal mass (C1) of the motor, iron thermal mass (C2) of the motor, a first thermal resistance (R1) coupled between the copper (C1) and iron (C2) thermal mass, wherein node 1 is a circuit point between copper thermal mass (C1) and first thermal resistance (R1) and node 2 is a circuit point between iron thermal mass (C2) and first thermal resistance (R1), a first voltage source (E1) indicative of ambient temperature of the motor, a second thermal resistance (R2) coupled between the iron thermal mass (C2) and the first voltage source (E1), wherein node 3 is a circuit point between second thermal resistance (R2) and first voltage source (E1), a third thermal resistance (R3) and switching means for opening and closing an electrical circuit, said switching means having an input and an output, wherein said third thermal resistance (R3) is coupled between the iron thermal mass (C2) and the input of said switching means and the output of said switching means is coupled to said first voltage source, a second voltage source (E2) indicative of the temperature of the windings of the motor and a fourth thermal resistance (R4) coupled between the copper thermal mass (C1) and the second voltage source (E2), and further wherein node 4 is a circuit point between fourth thermal resistance (R4) and a second voltage source (E2), and wherein each of first (E1) and second (E2) voltage sources, copper thermal mass (C1) and iron thermal mass (C2) is referenced to the same electrical potential;   providing the microprocessor with a data base for said motor including at least:   power losses (P i ) within the motor for each node i of the thermal analog, and   thermal time constants for the combination of each thermal mass and thermal resistance coupled directly thereto;   constantly determining ambient temperature (E1) of the motor operating environment;   constantly providing the microprocessor with said environment temperature (E1);   constantly determining temperature (E2) of the windings of the motor;   constantly providing the microprocessor with said windings temperature (E2);   repetitively calculating in the microprocessor, at predetermined intervals Δt, the following equation over all nodes i: ##EQU6## wherein: N=number of nodes i, P i  =power loss at node i,   T i  =temperature at node i,   T j  =temperature at node j,   α i  =Δt/C i     β ij  =Δt/(R ij  ·C i )   ΔT i  =temperature change at node i over interval Δt;     adding each calculated value of temperature change ΔT i  to a previous value of node i temperature T iold  to create T inew , wherein T inew  is used as the value of T iold  for the next interval Δt;   repetitively comparing in the microprocessor at said predetermined intervals the temperature T inew  at node i with a predetermined temperature limit T iM  for node i; and   removing power supplied to said motor when temperature T inew  equals or exceeds the predetermined temperature limit T iM  for node i.   
     
     
       2. The method as in claim 1 wherein switch S1 is closed when the rotor of said motor is rotating and is open when the rotor of said motor is not rotating. 
     
     
       3. The method as in claim 1 wherein the value of first voltage source (E1) is supplied from a resistance temperature device (RTD) imbedded in the motor windings. 
     
     
       4. The method of claim 3 wherein the coefficient for determining heat transferred to node 1 from node 4 (β 14 ) is equal to predetermined interval Δt divided by the thermal time constant τ RTD  of the RTD. 
     
     
       5. The method as in claim 1, wherein the coefficient for determining heat transferred to node 1 from node 2(β 12 ) is equal to   Δt/τ.sub.1     wherein τ 1  is the motor short time constant.   
     
     
       6. The method as in claim 1 wherein the coefficient for determining heat transferred to node 2 from node 1 (β 21 ) is equal to ##EQU7## wherein t C  is the motor cold stall time; t H  is the motor hot stall time;   τ 1  is the motor short time constant;   τ 2RUN  is the motor long time constant with the motor running;   LR is the motor locked rotor current; and   FLAMPS is the motor full load amps.   
     
     
       7. The method as in claim 1 wherein the coefficient for determining heat transferred to node 2 from node 3, during times that the motor is running, (β 23RUN ) is equal to ##EQU8## wherein τ 2RUN  is the motor long time constant with motor running. 
     
     
       8. The method as in claim 1 wherein the coefficient for determining heat transferred to node 2 from node 3, during times that the motor is not running, (β 23OFF ) is equal to ##EQU9## wherein τ 2OFF  is the motor long time constant with motor off. 
     
     
       9. A thermal model of an induction motor comprising: a first capacitor indicative of the copper thermal mass of the motor;   a second capacitor indicative of the iron thermal mass of the motor;   a first resistor, indicative of the thermal resistance between the iron and copper thermal masses of the motor, said first resistor coupled between one side of said first and second capacitor, respectively;   a first voltage source, indicative of ambient temperature of the motor and a second resistor, indicative of the thermal resistance between the iron thermal mass and the ambient environment of the motor, said first voltage source having one side coupled through said second resistor to the one side of said second capacitor;   a series combination of a third resistor and a switch, said combination coupled between the one side of said second capacitor and said first voltage source, respectively; and   a second voltage source, indicative of winding temperature of the motor and a fourth resistor indicative of the thermal resistance between the copper thermal mass and a winding temperature sensing device, said second voltage source coupled through said fourth resistor to the one side of said first capacitor,   wherein the other side of each said first and second voltage sources and each said first and second capacitors is connected to the same reference potential.   
     
     
       10. The model as in claim 9 further comprising protection means coupled to the junction of said first capacitor and said first resistor for interrupting power to the motor when voltage at the junction of said first capacitor and said first resistor exceeds a predetermined threshold. 
     
     
       11. The model as in claim 9 further comprising protection means coupled to the junction of said second capacitor and said first resistor for interrupting power to the motor when the voltage at the junction of said second capacitor and said first resistor exceeds a predetermined threshold. 
     
     
       12. The model as in claim 9 further comprising first protection means coupled to the junction of said first capacitor and said first resistor for interrupting power to the motor when voltage at the junction of said first capacitor and said first resistor exceeds a first predetermined threshold and second protection means coupled to the junction of said second capacitor and said first resistor for interrupting power to the motor when the voltage at the junction of said second capacitor and said first resistor exceeds a second predetermined threshold. 
     
     
       13. A method for simulating a thermal model to determine the temperature T i  of each thermal mass or node N i  of said model at incremental time intervals Δt, where the temperature T i  of several thermal masses of said model can be measured, and wherein the heat loss P i  at each node N i  is known, said method being particularly suitable for implementation using a general purpose microprocessor, said method comprising the steps of: (a) defining a reciprocal time-normalized thermal capacity α 1  for each node N i  wherein the reciprocal time-normalized thermal capacity α i  represents the amount of temperature rise during said time interval Δt proportional to the heat loss P i  to said node N i , that is to say:   α.sub.i =Δt/C.sub.i ;       (b) defining a heat transfer coefficients β ij  for each node N i  and its adjoining nodes N j  wherein each said coefficient β ij  represents the proportion of heat transferred to node N i  due to a temperature difference between node N i  and its adjoining node N j , that is to say:   β.sub.ij =Δt/(R.sub.ij ·C.sub.i),     and wherein:     β.sub.ij is not equal to β.sub.ji ;       (c) determining the value of said measured temperatures T i  at each said interval Δt;   (d) determining the change in temperature ΔT i  of each remaining node N i  at each said interval Δt as: ##EQU10## (e) determining the new temperature T inew  of each node N i  at each said interval Δt as:   T.sub.inew =T.sub.i +ΔT.sub.i ;       (f) revising the temperature T i  of each node N i  to reflect the new temperature as:   T.sub.i =T.sub.inew ; and       (g) repeating the steps (d) through (g) at each said interval Δt.   
     
     
       14. A method of protecting an induction motor from excessive thermal overloads with the aid of a general purpose microprocessor, comprising: selecting an analog model of said induction motor to be simulated by said microprocessor at incremental time intervals Δt, said model including thermal masses represented by nodes N i , each said thermal mass or node N i  having a thermal capacity C i  and power losses P i , the thermal resistance between two nodes N i  and N j  being R ij  wherein:   R.sub.ij =R.sub.ji ;       using said model to define a reciprocal time-normalized thermal capacity α i  for each node N i  as:   α.sub.i =Δt/C.sub.i ;       wherein said model to define heat transfer coefficients β ij , each representing the heat transferred to node N i  from its adjoining node N j , as:   β.sub.ij =Δt/(R.sub.ij ·C.sub.i);       simulating said model to determine the temperatures T i  of each node N i  at each time interval Δt, said simulating step comprising the substeps of:   (a) measuring the value of several temperatures T i  of certain nodes N i  at each interval Δt;   (b) determining the change in temperature ΔT i  for each remaining node N i  over each interval Δt, wherein:   ΔT.sub.i =α.sub.i ·P.sub.i -Σβ.sub.ij ·(T.sub.i -T.sub.j);       (c) determining the new temperature T inew  for each node N i , wherein:   T.sub.inew =T.sub.i +ΔT.sub.i ;       (d) defining the temperature of each node at the end of each time interval Δt as:   T.sub.i =T.sub.inew ; and       (e) comparing the temperature T i  of each node N i  to a predetermined temperature limit for that node, and discontinuing power to said motor if said temperature T i  is greater than said predetermined limit.